Radical-Locator Polynomials and Row-Echelon Partial Syndrome Matrices With Applications to Decoding Cyclic Codes
Chong‐Dao Lee · IEEE Transactions on Information Theory · 2018
Partial syndrome matrices and weak-locator polynomials have received considerable attention in recent years due to their applications in decoding cyclic codes. The technical contribution of this paper is threefold: (1) cyclic codes can be decoded by the newly proposed partial syndrome matrices, which generalize the previously known results on the determination of error positions; (2) a new type of polynomial associated with error locations, called radical-locator polynomial, is defined, which includes the weak-locator polynomial as a special case; and (3) a novel class of matrices with many zero entries, called row-echelon partial syndrome matrices, is presented, based on the Newton identities, for efficiently decoding cyclic codes. It is also shown that the radical-locator polynomials can be obtained from the determinants of the above-mentioned (row-echelon) partial syndrome matrices.